Question

You are testing internal controls by testing the attributes of the population. Your in-charge accountant has directed you to use a five percent acceptable risk of assessing control risk too low (what the book shortens to ARACR). Based on a sample already drawn from the population, you estimate that the population has an exception rate of about 1.5% to 2.0%, but you are not sure what the true exception rate is; you just think that it is somewhere in that range. After discussion with the in-charge accountant, the two of you decide that for purposes of the audit, you can tolerate an exception rate of five percent, because there are additional controls which kick in later in the process.

Required:

a. What sample size do you need?

b. If you actually find five exceptions in your test of the sample, can you conclude that there is at least a 95% probability that the true exception rate in the population is five percent or lower? Explain your answer. (Teacher's note: A simple "yes" or "no" without further explanation will receive a grade of zero. Even if your answer is correct, you will not receive credit unless you can properly explain your answer.)

Answer 1

Before going into the specific answer let us know some of the basic terms useful for answering the question.

SAMPLING ERROR -   It is an inherent error that results from testing less than the entire population.

NON SAMPLING ERROR - This type of errors occur when audit test do not detect errors that existed in the sample.

It may be due to - Auditor's failure to recognize exceptions or

- Inappropriate / Ineffective audit procedures.

ATTRIBUTE - It means characteristics being tested for in a population.

EXCEPTION - It occurs when the attribute being tested for is absent or not found.

EXCEPTION RATE - The % of items in a population that include exceptions in prescribed controls.

SAMPLE EXCEPTION RATE- Number of exceptions in the sample/ Sample size

Now moving forward with the question,

A Low ARACR( Acceptable Risk of Assessing Control Risk too low ) = The test of controls are important and will correspond to a low assessed control risk and reduced substantive test of details of balances. A larger sample size is required to lower the risk.

For determining the initial Sample Size, factors are used.

1) POPULATION SIZE

2) TOLERANCE EXCEPTION RATE ( TER )

3) ACCEPTABLE RISK OF ASSESSING CONTROL RISK ( ARACR)

4)ESTIMATE THE POPULATION EXCEPTION RATE ( EPER )

In attributes sampling, auditors usually use computer programs or tables developed from statistical formulas to determine the sample size.

Now let us analyse the relationship of above mentioned factors in relation to sample size.

AN INCREASE IN ARACR----------- A DECREASE IN INITIAL SAMPLE SIZE

AN INCREASE IN TER----------- A DECREASE IN INITIAL SAMPLE SIZE

AN INCREASE IN EPER----------- AN INCREASE IN INITIAL SAMPLE SIZE

AN INCREASE IN POPULATION SIZE------- AN INCREASE IN INITIAL SAMPLE SIZE.

In short ARACR & TER have the greatest effect on Initial sample size.

For the second part of the question, we cannot conclude that there is at least a 95% probability that the true exception rate in the population is 5% or lower as there are various other factors also which determine the same. The above explanations substantiate the answer.Moreover on an another angle it can also be stated that it depends on the size of the population being studied or sampled. Adding further it depends on how variable the population is in the parameters being used.